@christianp I've only given this two minutes thought as I'm currently a bit busy, but for those numbers where you claim it does not go to 1, do you have a proof? Are such proofs quite general?

@christianp ... and there are only finitely many possibilities ... fair enough. Seems easy enough to compute lots of values and sufficiently well-defined. Good luck with the bureaucracy of the OEIS ... be prepared to be patient.

Christian Lawson-Perfect@christianp@mathstodon.xyz@ColinTheMathmo the behaviour depends on (N, T mod N). So if I get to such a pair I've seen before, it must loop.